Triangle Inequality Theorem Worksheet
Explore the Triangle Inequality Theorem with this worksheet, featuring questions on determining valid triangle side lengths and applying the theorem to solve problems.
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Triangle Inequality Theorem
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. Which of the following sets of side lengths can form a triangle?
3 cm, 4 cm, 8 cm
5 cm, 7 cm, 12 cm
6 cm, 9 cm, 10 cm
2 cm, 3 cm, 5 cm
2. If two sides of a triangle are 10 inches and 15 inches long, which of the following could be the length of the third side?
4 inches
25 inches
5 inches
20 inches
3. The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be than the length of the third side.
4. If a triangle has sides of length 'a', 'b', and 'c', then it must be true that a + b > c, a + c > b, and .
5. A triangle has two sides with lengths 7 cm and 11 cm. What is the range of possible lengths for the third side?
6. Can a triangle be formed with side lengths 14 mm, 6 mm, and 8 mm? Justify your answer using the Triangle Inequality Theorem.
7. A triangle with side lengths 1 cm, 2 cm, and 3 cm can exist.
True
False
8. If the sum of two sides of a triangle is equal to the third side, it forms a degenerate triangle.
True
False
Match the side lengths with whether they can form a triangle or not.
9. 5, 5, 5
a. Cannot form a triangle
10. 1, 2, 4
b. Can form a triangle
11. 10, 10, 20
c. Can form an equilateral triangle